Three-layered relativistic hybrid star with distinct equation of states

Abstract

In this paper, we are proposing a three-layered hybrid compact star model with a distinct equation of states (EOSs) in the realm of general relativity. The core is assumed to be quark matter described by the MIT-bag model, an intermediate layer filled with neutron liquid and a thin envelope of matter satisfying a quadratic EoS. Three pairs of interfaces are matched by using Darmois–Israel conditions. For better and easier tuning, we have chosen $\alpha$ as a free parameter for core, k for intermediate layer and g and t for envelope, while the rest of the constant parameters are linked with mass and radius. Most of the physical parameters such as density, pressures and EoS parameters are continuous in all the three regions; however, $v_t^2$ and stability factor are discontinuous. This is because of the non-differentiability of $p_t$’s at the interfaces. Hence, stability is not defined at the interfaces. Further, matching of $p_t$’s can be performed by tuning suitable values of the free parameters $\alpha , ~k, ~g$ and t. Further, the most prevailing aspect of this method is that we can arbitrarily choose the radii of each region. As per Buchler and Barkat (PRL 27: 48, 1971) and Baym et al.(PRL 175: 225, 1971) , there exists a smooth transition density between quark core and intermediate neutron-liquid layer at about $\rho > 10^{14}~{\mathrm{g/cc}}$. Our calculation shows that the smooth transition density is at about $\rho _I=4.16 \times 10^{14}~ {\mathrm{g/cc}}$ which is in good agreement with the above prediction.